Question

3. What values of the angular momentum (l) and magnetic (ml) quantum numbers are allowed for a principal quantum number (n) of 4? How many orbitals are allowed?

Answer 1

When n = 4 , l = 0 ≤ ℓ ≤ n − 1 that is 0,1,2,3

ml values = −ℓ ≤ m_ℓ ≤ ℓ

                                                           orbitals allowed

so if l = 0 , m =0,                                       1(s orbital)

When l =1, ml = -1,0,+1                                3 (px,py,pz orbitals)

when l = 2 , ml = -2,-1,0,+1,+2                     5 (dxy,dyz,dzx,dx2,dx2-y2)

when l = 3 , ml = -3,-2,-1,0,1,2,3                  7 (f orbitals0